Complications With Shading
This is not a clipping issue. Clipping error would make it look like you had sliced off the front or back of the mesh in a plane perfectly parallel with the screen, not making things look like they were in front of other things.
The node setup is incorrect:

The texture coordinates for that hair thing should NEVER be reflection. Disconnect that, and leave it (it will default to the UV map, which is what you want). Reflection texture coronets make it look as if the mesh is reflecting whatever the texture is.
Emission has nothing to do with things being shaped differently, which is why I think you connected to it. Emission is for things that glow.
You have an extra copy of the Head’s diffuse color texture, which can be deleted.

It also looks as if you may be using alpha blend for your material alpha settings. Use alpha hashed instead, as alpha blend can have sorting issues which would make things appear in front of other things arbitrarily.